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Does it make sense to add more factors such as Quality Minus Junk (QMJ) and Betting Against Beta (BAB) in the Fama-French-Carhart model? Also, if anyone can point me to an article it would be appreciated.

$$r=α+R_f+β_m(R_m−R_f)+β_s⋅SMB+β_v⋅HML+β_{umd}⋅UMD$$

Would add QMJ and BAB to the regression.

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    $\begingroup$ Why do you want to do that? To better explain the cross-section of stock returns? Or to evaluate actively managed portfolios? In principle, you can add as many factors as you want to. $\endgroup$
    – Kevin
    Jun 25, 2020 at 0:02
  • $\begingroup$ The idea would be to understand better stock returns. I am wondering if it will yield better coefficients and maybe evaluate actively managed portfolio having a low number of stocks $\endgroup$
    – Circus_beta
    Jun 25, 2020 at 1:43

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This depends on your data and whether it would isolate the new factors completely.

Adding more factors is sometimes difficult as it can decrease the strength of your model and muddle up the previously "good" model, such as Carhart.

QMJ is used to check for quality, but since you are adding other factor in addition to it, you could do other robustness checks instead of QMJ.

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    $\begingroup$ Could you please elaborate on your last point? $\endgroup$
    – Circus_beta
    Jun 25, 2020 at 15:03
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You can add the factors and perform the regression but be careful while assessing the effect of adding more parameters to your model, event though the basic model power may seem to increase(R-square) but checking the parameters in depth(p-value, t-stat) is always useful.
In general, adding more than 5 factors to your model counters your goal. So be careful on which factors to use.

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The most often used additional factor is Pastor-Stambaugh.

The Fama-French model is augmented with a proxy for the Pastor-Stambaugh liquidity factor. r = RF + βmkt (RM - RF) + βS x SMB + βV x HML + βL x LIQ

You could check the replication issue at Critical Finance

https://www.nowpublishers.com/article/Details/CFR-0074 https://www.nowpublishers.com/article/Details/CFR-0075

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I do not believe adding both of these factors would be the best choice given that the BAB factor is already taken into account in the safety subcomponent of the QMJ factor.

I would highly recommend looking into Taming the Factor Zoo by Feng, Giglio and Xiu (2020), summarized here by AQR as it aims to help with answering precisely your question.

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